Charge and reduce: A fixed-parameter algorithm for String-to-String Correction
String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we...
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| Published in: | Discrete optimization Vol. 8; no. 1; pp. 41 - 49 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.02.2011
|
| Subjects: | |
| ISSN: | 1572-5286, 1873-636X |
| Online Access: | Get full text |
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| Summary: | String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we consider a classic string distance problem, the
N
P
-complete
String-to-String Correction problem, first studied by Wagner some 35 years ago. In this problem, we are asked whether it is possible to transform string
x
into string
y
with at most
k
operations on
x
, where permitted operations are single-character deletions and adjacent character exchanges. We prove that
String-to-String Correction is fixed-parameter tractable, for parameter
k
, and present a simple fixed-parameter algorithm that solves the problem in
O
(
2
k
n
)
time. We also devise a bounded search tree algorithm, and introduce a bookkeeping technique that we call
charge and reduce. This leads to an algorithm whose running time is
O
(
1.618
1
k
n
)
. |
|---|---|
| ISSN: | 1572-5286 1873-636X |
| DOI: | 10.1016/j.disopt.2010.10.003 |